SPHERICAL DISTORTION. 
convexity renders a diminished diameter necessary it also pro¬ 
duces a diminished focal distance ; and since the aperture 
(that is, the angle formed by lines drawn from the principal focus 
to the extremities of a diameter of the lens) increases with the 
decrease of the focal distance, this decrease may compensate for 
the decrease of the diameter, so that the aperture may not he 
diminished. But in fact the decrease of focal distance, much more 
than compensates for the decrease of the diameter, and in good 
lenses the aperture is much greater for small lenses of high magni¬ 
fying power, than for larger ones with lower magnifying power. 
It is owing to this, that great magnifying powers can be 
obtained without rendering the illumination of the image 
injuriously faint, as it would be, unless the aperture of the lens 
on which it depends were augmented in some degree proportionate 
to the increase of the power. 
46. SPHERICAL DISTORTION'. 
Independently of the spherical aberration properly so called, 
there is another optical effect produced in the image, depending 
on the form of the lens, which requires notice. 
In the preceding paragraphs it has been assumed that the form 
of the image is that of the object, and when the image is small 
this may be considered as practically true. But when the image 
is considerably amplified the form differs sensibly from that of 
the object. 
If an object which is straight or flat be presented to a convex 
lens, outside its principal focus, so that a real image shall be pro¬ 
duced on the other side of the lens, the image will not be flat but 
curved, with its concavity towards the lens. If the object were 
curved with its convexity towards the lens, its image would be 
also curved, but with its concavity towards the lens, and the 
curvature of the image would in that case be greater than that of 
the object. 
If the object were concave towards the lens, its image would 
be also concave towards the lens, but with less curvature than 
the object. 
47. If the curvature of the object be supposed gradually to 
increase, the concavity still being presented towards the lens, 
the image will be also concave towards the lens, but its curvature 
will diminish as that of the object increases, and when the 
curvature of the object increases to a certain point, the image will 
become straight or flat. 
If the curvature of the object still continue to increase, the 
image will become convex towards the lens, and its curvature 
will increase with that of the object. 
105 
